Games that get much better after playing them are usually
Multiplayer shooters which have serious competitions going on in multiplayer servers.
Basically all strategy games get boring untill you play with humans or competitively in a server.
Games with a long intro.
Personally, these games fell into that category:
Starcraft, CS 1.6, some mods of Half-life.
If you are looking for games Ross, here is my tips:
If you love multiplayer, teamplay, community, amazing gameplay at times I suggest you pick only 2-3 multiplayer games which have a good community, Ross, and become at least a good sport in them, pick one server or so, and play for competition. You won't ever feel like you need to search for more than 2-3 multiplayer games
. I'm still stuck with either Starcraft 1-2 or CS on multiplayer occasionally. No players can competitively play on two different games at the same time.
For singleplayer games, I suggest Stalker, all Valve games of course, S.W.A.T., FEAR and basically just search for more games of the famous companies. Subscribe to them. Try the early 2000's and late 1990's too, best years of singleplayer.
For short fun Arcade just search DOS classic games on google or play some of the racing games. In case of DOS don't get turned off by the graphics, the games almost always provide what their genre promises.